%load_ext autoreload
%autoreload 2

import sys
sys.path.append("..")

import pandas as pd
from numpy.random import random
import datetime as dt
from statsmodels.tsa.stattools import acf, pacf
import statsmodels.api as sm
from scipy.signal import periodogram
import math

from pytsviz.viz import *

dataset_size=366

n_features = 3

Target series

t_axis = pd.date_range(start='1/1/2020', periods = dataset_size, freq="D", name="t")

y = (1 + random(dataset_size)) * np.linspace(6, 9, dataset_size) + \
    (1 + random(dataset_size)) * np.sin(np.linspace(0, 10*np.pi, dataset_size)) + \
    (1.5 + random(dataset_size)) * np.cos(np.linspace(0, 5.4*np.pi, dataset_size))
ts = pd.Series(index=t_axis, data=y, name="y")
ts_df = ts.to_frame()

Features

feat_matrix = random((n_features, dataset_size))
feat_df = pd.DataFrame(index=t_axis, data={f"x_{i}": feat_matrix[i] for i in range(n_features)})

Forecast

ext_t_axis = pd.date_range(start='2/1/2020', periods = dataset_size, freq="D", name="t")

y_hat = y * (1 + 0.1 * random())

forecast = pd.Series(index=ext_t_axis, data=y_hat, name="y_hat")
forecast_df = forecast.to_frame()

c_lower = [y_hat[i] - (0.001 * i) ** 1.2 for i in range(len(y_hat))]
c_upper = [y_hat[i] + (0.001 * i) ** 1.2 for i in range(len(y_hat))]
confidence_df = pd.DataFrame(index=ext_t_axis, data={"lower confidence": c_lower, "upper confidence": c_upper})

total_df = pd.concat([ts, feat_df, forecast_df, confidence_df], axis = 1)

total_df

	y	x_0	x_1	x_2	y_hat	lower confidence	upper confidence
t
2020-01-01	8.079131	0.242302	0.557478	0.601941	NaN	NaN	NaN
2020-01-02	10.650662	0.929234	0.557489	0.376543	NaN	NaN	NaN
2020-01-03	12.083600	0.809896	0.709311	0.864642	NaN	NaN	NaN
2020-01-04	10.490799	0.226948	0.019853	0.784072	NaN	NaN	NaN
2020-01-05	9.314644	0.217527	0.305872	0.584400	NaN	NaN	NaN
...	...	...	...	...	...	...	...
2021-01-27	NaN	NaN	NaN	NaN	11.590459	11.296011	11.884907
2021-01-28	NaN	NaN	NaN	NaN	10.132183	9.836756	10.427610
2021-01-29	NaN	NaN	NaN	NaN	14.192122	13.895716	14.488529
2021-01-30	NaN	NaN	NaN	NaN	17.808586	17.511200	18.105973
2021-01-31	NaN	NaN	NaN	NaN	13.055010	12.756642	13.353377

397 rows × 7 columns

fig = plot_ts(total_df, y_cols=["y", "x_0"], tf="log", tf_args = (np.e,), keep_original=True)

func1 = lambda x : x.isocalendar().week
func2 = lambda x : x.isocalendar().day

plot_seasonal_ts(ts_df, period="month", subplots=True)

plot_decomposed_ts(ts_df, method = "STL", subplots = True)

inverted_df = pd.DataFrame(total_df.values[::-1], total_df.index, total_df.columns)
#forecast_plot(inverted_df, ts_col = "y", fc_cols = ["y_hat"], lower_col = "lower confidence", upper_col = "upper confidence")

y_hat_2 = pd.Series(data=y_hat*0.9, index = ext_t_axis, name = "y_hat_2")
multiple_fc_df = pd.concat([total_df, y_hat_2], axis = 1)
plot_forecast(multiple_fc_df, y_col = "y", fc_cols = ["y_hat"], upper_col = "upper confidence", lower_col = "lower confidence")

plot_scatter_matrix(total_df, var1 = "x_0", var2="y", lags1 = [5, 10, 15])

plot_scatter_fit(total_df, "x_0", "x_1", fit = "summary")

                            OLS Regression Results
==============================================================================
Dep. Variable:                      y   R-squared:                       0.000
Model:                            OLS   Adj. R-squared:                 -0.002
Method:                 Least Squares   F-statistic:                    0.1396
Date:                Tue, 09 Mar 2021   Prob (F-statistic):              0.709
Time:                        11:29:20   Log-Likelihood:                -49.025
No. Observations:                 366   AIC:                             102.0
Df Residuals:                     364   BIC:                             109.9
Df Model:                           1
Covariance Type:            nonrobust
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.4909      0.029     16.660      0.000       0.433       0.549
x1            -0.0190      0.051     -0.374      0.709      -0.119       0.081
==============================================================================
Omnibus:                      119.146   Durbin-Watson:                   1.808
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               18.815
Skew:                           0.063   Prob(JB):                     8.21e-05
Kurtosis:                       1.896   Cond. No.                         4.46
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

plot_acf(ts_df, show_threshold = True)

plot_acf(ts_df, partial=True, alpha = 0.1, show_threshold = True)

plot_psd(ts_df, scaling="spectrum")

plot_distribution(total_df, bins=100, title="Distribution")

arparams = np.array([.75, -.25])
maparams = np.array([.65, .35])
ar = np.r_[1, -arparams] # add zero-lag and negate
ma = np.r_[1, maparams] # add zero-lag
arma_process = sm.tsa.ArmaProcess(ar, ma)

plot_inverse_arma_roots(arma_process)

plot_extended_scatter_matrix(total_df.dropna(), y_cols=["y", "x_1", "x_2"])

plot_ts_overview(ts_df)

plot_ts_analysis(ts_df)

plot_gof(total_df, "y", "y_hat")